The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincaré polynomials.
Bibliographical notePublisher Copyright:
© 2015 American Mathematical Society.
- Betti numbers
- Components of a Springer fiber
- Flag manifolds
- Grassmannian varieties
- Iterated bundles
ASJC Scopus subject areas
- Mathematics (all)
- Applied Mathematics